Real Numbers - Lesson Summary

Real Numbers The collection of all rational numbers and irrational numbers together is the set of real numbers. It is represented by R. A real number is either a rational number or an irrational number.

In a division, if remainder becomes zero after certain stage, then the decimal expansion is terminating. If the remainder never becomes zero but repeats after certain stage, then the decimal expansion is non-terminating recurring.

A rational number can be expressed as its decimal expansion. The decimal expansion of a rational number is either terminating or non-terminating recurring. The decimal expansion of an irrational number is non-terminating non-recurring. Every real number can be represented on a number line uniquely. Conversely every point on the number line represents one and only one real number.

The process of visualisation of representing a decimal expansion on the number line is known as the process of successive magnification.